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Factorize : $(x+y+z)^p-[(-x+y+z)^p+(x-y+z)^p+(x+y-z)^p]$ where $p$ is an odd prime.

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#diophantine-equations #factoring #binomial-theorem
72
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Divisibility of a number $N$ by $4,7,9$

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#algebra-precalculus #elementary-number-theory #binomial-coefficients #binomial-theorem
156
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Binomial theorem for trace of vectors

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#linear-algebra #binomial-theorem
56
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Prove $\sum_{k=0}^n {n\choose k} = 2^n$ and $\sum_{k=0}^n (-1)^{k} {n\choose k}=0$ for $n \ge 1$

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#binomial-coefficients #binomial-theorem
303
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Find the Coefficient of $x^3$ in $(2+x^2)^3 (3+2x)^7$

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#combinatorics #algebra-precalculus #binomial-coefficients #binomial-theorem
364
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Evaluate sum using generating function

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#summation #binomial-coefficients #generating-functions #binomial-theorem
150
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Prove that such a function exists that mimics binomial theorem

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#calculus #sequences-and-series #combinatorics #analysis #binomial-theorem
1.2k
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Closed form of to calculate variation of Pascal's triangle

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#combinatorics #binomial-coefficients #binomial-theorem #stirling-numbers
105
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Prove the equality

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#summation #binomial-coefficients #binomial-theorem
163
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Prove equality between binomial coefficients.

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#binomial-coefficients #binomial-theorem
80
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Represent $f(x)=\frac{1}{(1-x^2)^4}$ as a power series

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#sequences-and-series #binomial-coefficients #binomial-theorem
111
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Prove binomial equation

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#summation #binomial-theorem
192
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A summation series of binomial coefficients

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#algebra-precalculus #binomial-coefficients #binomial-theorem
3.7k
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How to substitute x into binomial

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#binomial-theorem
53
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Determine maximal addend in Newton Binomial Expansion.

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#calculus #algebra-precalculus #binomial-coefficients #binomial-theorem

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